16 November 2012

The 85th Percentile Folly

It's not like we needed any more proof that we live in car-centric cities. When you start scratching just a little below the surface, however, you start to discover that we are not so much citizens in cities but rather a flock of reluctant characters in The Matrix.

You discover that we live in cities that are controlled by bizarre and often outdated mathematical theories, models and engineering “solutions” that continue to be used despite the fact that they are of little use to modern cities.

One of them is called The 85th Percentile. It's a method that cities all over the planet use to determine speed limits. It's the standard. Nobody questions it. Certainly not the engineers and planners who, for decades, have been served it up and who have swallowed it whole during their studies. Which reminds us of the old traffic engineer joke: Why did the engineer cross the road? Because that's what they did last year.

The concept is rather simple: the speed limit of a road is set by determining the speed of 85% of cars that go down it. In other words, the speed limit is solely set by the speed of drivers, and this is the basic rule that determines traffic speeds worldwide. Including the street outside your home.

It can, of course, be revised but that rarely happens. The engineers will just shrug and say that The 85th Percentile method is the only method and can't be changed. The numbers don't lie. The problem is that human beings are not numbers.

Here's the tricky part of the 85th percentile method. It assumes the following:
• «The large majority of drivers are reasonable and prudent, do not want to have a crash and desire to reach their destination in the shortest possible time;
• A speed at or below which 85 % of people drive at any given location under good weather and visibility conditions may be considered as the maximum safe speed for that location».

If they're assuming that the large majority of drivers are reasonable and prudent, then what about the rest of the drivers? I guess that's what living in The Matrix is like: assume that everything is going to be fine by handing over complete power of our streets to motorists. AND mixing anthropological assumptions with pseudo-science. Not generally regarded as a good idea.

When someone gets their driving licence they should be warned that “you now have a licence to carry a weapon and kill people”. You don't need a degree in anything to know that speed kills and injures. Here is a rather telling graph about the danger of speed:

This, on the other hand, is the traffic engineer's perception of “safety” and speed. Looking at the graph, their perception is rather different and rather out of date:

Imagine a street where the average speed is 50 km/h. If the speed is reduced by 5 km/h then, according to this archaic model, the drivers are allegedly exposed to a higher risk. What is most shocking is that this entire concept completely ignores pedestrians and cyclists. Another horrific conclusion from this graph is that when you increase the speed, the crash risk is alleged to be less than for slow speeds.

All of this seems suspiciously like an argument to build more highways and freeways – because “with more speed comes more security”, as they (once) said.

The graph is still touted as the “latest research” is called The Solomon Curve. We were looking into it here at the office and we all guessed how old it was. None of us were close – guessing between 15 and 30 years old. In reality, it is based on a study by David Solomon back in 1964.

It is still wholly endorsed by the U.S. Department of Commerce and the Bureau of Public Roads, which was administrated - at the time of the study - by Rex Whitton. He was also – surprise, surprise – a Federal Highway Administrator. Okay, we're not surprised.

Basically, a study from 1964 remains the main argument to build more highways and freeways with faster speeds where the ends justify the means. Even if the means ignore vulnerable groups such as pedestrians and cyclists. Even if the study is now also used to serve the automobile in densely-populated urban areas, far from any freeway.

I'm glad you've written about this - it's cited in the UK as being relevant for use in setting speed limits on residential back roads!!!I've always disagreed with it - when a driver selects their speed they are doing so according to risk TO THEMSELVES and have no intrinsic consideration for external risk to others. I'm surprised there hasn't been more research into the way speed is perceived by drivers. In a recent edition of 'Top Gear' (BBC) one of the presenters tried to get out of a Bugatti Veyron they had been driving at over 200mph while it was still moving at 70 mph! I know from my own experience that driving a Fiat Punto 1.2 Auto means I automatically travel at much lower speed than in a 3.0 litre V8 BMW!The 85th percentile IS useful for determining what will be an easily COMPLIANT speed limit but only has use on freeways (motorways) where vulnerable road users and junctions are absent.This dangerous and completely misused method HAS to be shown to be irrelevant - otherwise we may never have safe limits in the UK.

The petition is now accepted for signature gathering and I think your platform could well help spread the idea and gather signatures. I also do not think I need to explain to your (nor to the other readers of your blog) why this is a very important petition. If you are curious or want a quick summary for other people to read there is also a nutshell-section on the website: http://en.30kmh.eu/why-30kmh-20-mph/

Research has clearly shown that the speed at which drivers travel is principally influenced by the characteristics of the street environment (refer to Learning from Best Practice Streetscape Design, 2007 and UK Manual for Streets 1 and 2). If the design of a street creates the perception that it is safe to travel at higher speeds drivers will do so, even if this conflicts with the posted speed limit. The irony of this seems tragically lost on most engineers as they seek eliminate risk to make streets 'safer. Clearer sightlines and wide carriageways do allow for greater driver reaction time/error correction. Whilst this approach is sensible on isolated roads, within urban areas it can be counter productive as it simply transfers risk to more vulnerable users. It is inevitable that pedestrians and vehicles will interact in urban environments. By creating larger, free flowing roads which prioritise vehicle movement, where this interaction occurs it is likely to happen at a much higher speed, thus increasing the severity of an accident.

I get the bell curve bit, showing distribution of sampled cases travelling at a given speed. I can imagine how it might well look more or less like that as it does seem to be a standard distrbution in most statistical samples (although there are usually bulges or spikes which spoil the symmetry)

What I don't get is the "risk curve". Where does that come from, apart from out of some overheated imagination of a petrol head? You know, like the bizarre claim that cars use more fuel when they drive more slowly, when the simple laws of physics (velocity stabilsises when thrust = resistance; resistance proportional to velocity^2) tell you otherwise.

All I can think of is that the hypothesis is that a slower vehicle is more likely to collide with a vehicle travelling at the median speed than anoher vehicle travelling at median speed is, because there is a speed differential in hte former but not the latter.

But of course there is another way of expressing that proposition - it is the faster (median speed) car which causes the risk, not the slower.

@SteveL , Thanks. The speed limits are indeed outrageously established.The other crazy aspect is that they do the same method even for smaller roads... Imagine the fact you pointed out but at 20mph: probably drivers would drive above the limit and then there would be 35mph limit instead, endangering pedestrians and cyclists a lot.

@crapbournemouthcyclist , I think we shouldn't focus only on establishing limits using a computer formula -- even for freeways. Every case is a different case. But this whole case reminds me of a basic rule that universities teach to economics students: "the market will solve its own problems, without external help". Look at the economy now. In this case it would be something like: "speed limits can be imposed by drivers therefore ignore the pedestrians". Look at the pedestrian fatality numbers. Indeed this has to be show irrelevant to modern planning and engineering.

@Maximilian Wollner , thanks for the heads up. Any time soon we will have fresh news on that.

@Jason Taylor , True. It's also ironic to leave pedestrians and cyclists out of the equation, whether for densely populated areas or not.

@Paul M , according to the Solomon study, he interviewed thousands of people... But what I think he meant was: imagine you are in a highway at 120 km/h on the far right lane. If a guy is driving in front of you at 80 km/h you have to change lanes, hence creating a risk of accident to you and others. So, according to the study, let's put everyone driving faster.

great article, but i think you are missing the point of the 85%ile rule. the 85%ile speed is the speed that 85% of drivers drive less than. So only 15% of people exceed this speed. The theory is that there should be a correlation between this speed and the speed limit. This allows that the 15% of people who exceed the speed limit can be prosecuted by the police.

What happens when the 85% speed and speed limit don't match is then the issue.

you correctly say that this is then used by some engineers or roads authorities to justify a speed limit change, but this should not be the case.

the difference in the speeds highlights a problem which should be solved by either raising the speed limit if that is appropriate or by traffic calming the street.

the 85%ile speed measures the signals given to motorists as to the appropriate speed to drive on the road. if the 85%ile speed is too high it means it is time to change the signals.

putting a 30km/hr speed limit on a wide road won't work because the signals are confusing, so if you want a 30km/hr zone, the street should be designed to be a 30km/hr street with narrow lane widths etc.

Apart from the (in most cases probably very difficult) redesigning of roads, I've wondered to myself about the effect of posting on speed limit signs the metres per second equivalent of the km/h equivalent (or the feet per second equivalent in miles per hour-language places).

A number n kilometres per hour is n thousands of metres per 3.6 thousands of seconds (60 s x 60 min = 3600 s). In other words, n km/h = n m/3.6 s. So in a collision, an object (all things being equal) or person hit by a motor vehicle will have that velocity transferred to it/them. At 10 km/h, they would go 10 m in 3.6 s, which means 2.8 m in one second. Multiply that by each multiple of 10 or 5 km/h and you get the picture.

At 30 km/h, the threshold before severe danger of fatality to people hit by a car, according to your graph, 30 m in 3.6 seconds translates to a victim flying 8.4 m in one second. A frightful prospect even at that speed. This also applies to loose objects inside a vehicle in a crash.

Adding m/s equivalents to speed limit signs, in other words showing impact speed equivalents, might have some effect on motorists, especially with occasional signs in strategic locations adding to the limit a graphic of a car, a "BLAM" graphic, and a dotted arc with a spread-eagled flying person/child at the end of it with the caption "(n) metres in 1 second". This could help to drive home the effect of hitting a pedestrian/cyclist AT that speed, let alone faster.

@ Unknown, Yes, it's in fact the speed of 85% of drivers that establishes the speed limit. My point was to focus on the lack of inclusion of the pedestrians' safety (or opinion) on this matter. If 85% of drivers go through a neighbourhood street at 80 km/h doesn't mean it's the correct speed, despite they can do it. It means it's probably unsafe for pedestrians.

Also, you're assuming that the signals are able to "control" those 85% who establish the speed limit -- which in some cases its not enough -- but you're also forgetting about the fact that the other 15% may kill people (assuming none of the 85% will kill as well).

In other words, you're thinking of the driver as an error-free machine instead of a human being prone to errors (which is normal, but in this case means lives).

Don't you think this method should be reviewed? Thanks for your comment.

@Kiwehtin, there's one flaw in the beginning of that calculation by saying that "all things being equal". So, in a collision:

Ec 0(car)+ Ec 0(person) = Ec (car) + Ec (person)

however,

Ec 0 (person) = 0, (considering the person is stopped before the crash)

and

Ec = 1/2mv^2

so

1/2 m0(car)*v0^2 + 0 = 1/2 m(car)*V(car)^2 + 1/2m(person)*v(person)^2

so assuming the car speed is the same before and right after the crash, then v0car = vcar (such as its mass), then:

m(car)*v(car)^2 = 1/2m(person)*v(person)^2,

so,

v(person)=root[(2m(car)*v(car)^2)/(m(person))]

In other words, not all things are equal. In this case, the mass of the car influences, its velocity and the persons mass.

You're also ignoring the force of gravity (F=9,81*(mass of body)) which will influence how far the projectile (in this case, the person hit) would go and which "pulls" the body down.

So it's not that linear how a victim will be projected after the crash because several forces are included. But correct me if I'm wrong as I'd happily loose my physics rustiness.

When it comes to replace the signs, I agree with everything that wakes the driver out of the numbness.

Guess I'm no "Neo", in that I've never questioned the 85% model; could also be that I knew I would just be a voice crying out in the wilderness....

Even with the fallacy you illustrate, about people's 'reliability and integrity', there is a core concept overlooked: once behind the steering wheel, people feel imbued with some sort of 'super-power' and thrills and excites them; THEY CAN GO AT INCREDIBLE SPEEDS! AND IT TAKES NEXT TO NO EFFORT! This feeling of 'enhancement' is a DRUG, and people become quickly addicted.

You cannot cure an addiction with half-hearted stopgap measures; what will be needed to break the addiction is a full-blown INTERVENTION, something no society is ready to tackle.

Automakers are fond of saying, "We build what our customers ask for, that's why cars are they way they are." Designing and building cars ACROSS the board with feeble acceleration, and holding that line in the face of consumer outcry, would have gone a long way -- but alas, that ship has sailed....

I wish I could remember who said: "There are two great tragedies in life: ONE, that you don't get everything you want; TWO, that you DO." I tell my kids regularly, "WANT does not equal NEED; I'll see to your NEEDS first, and if I feel your WANT is reasonable, I'll see what I can do for you." Since it's been shown (at least in America) that the average person stops emtionally maturing at about age 13, maybe people, ADULT people, shouldn't GET everything they want. The carnage caused by drivers (once again, in America: 4x people killed by accidents in cars than ON PURPOSE by GUNS!) is appalling.

@ Pedro Madruga: Yes, it's in fact the speed of 85% of drivers that establishes the speed limit.

That might be the case in some backward places, but luckily not in Europe. My very brief Google search confirms what I remember from the university (Germany): In Germany, but also in Denmark and Switzerland and I assume in other European countries too, a V85 higher than the speed limit is primarily seen as a call for traffic calming measures such as speed bumps or cameras.

The folly does not lie in using the 85th percentile. In fact, measuring it and comparing it to the posted speed limit provides the traffic planner with a valuable reality check. Is the road or street really being used as intended by the planner? The interesting part starts when the answer to that question is no. Should we then try accommodate the unintended use or should we try to discourage it? This general question extends to other situations, too. Should we widen the streets when there is congestion? Should we build more parking spaces when there are too many parking offenders? The actual folly lies in always trying to accommodate motorized traffic, in believing that to be desirable or even possible. Luckily we seem to be moving beyond that.

Pedro Madru about the Solomon curve:"If the speed limit is reduced by 5 km/h then, according to this archaic model, the drivers are allegedly exposed to a higher risk. […] Another horrific conclusion from this graph is that when you increase the speed limit, the crash risk is alleged to be less than for slow speeds."

Now this is one ridiculous misinterpretation of a graph. Where do you find anything in there about speed limits? Let alone that increasing the speed limit would reduce the crash risk?

What this diagram actually says is that cars are more at risk when traveling much faster or much slower than all the other cars on that road. That sounds about right, at least for the main rural highways that Solomon’s report covers. The graph does not endorse or justify speeding. Solomon’s report actually says that higher speeds lead to more severe accidents.

”What is most shocking is that this entire concept completely ignores pedestrians and cyclists.”

Solomon’s report deals with main rural highways. Look, it says so right on the front page! How should it have any significance for pedestrians or cyclists?

Solomon’s report might be outdated by now and certainly not applicable to urban traffic, but all in all I am tempted to say that I find it much less deserving of the mark TOP STUPID than your dealing with it.

» "That might be the case in some backward places, but luckily not in Europe. My very brief Google search confirms what I remember from the university (Germany): In Germany, but also in Denmark and Switzerland and I assume in other European countries too (...)"

From what you're saying, traffic engineers in Europe apply a different rule than the ones in some "backward places". I'm interested in learning that, please.

» "The folly does not lie in using the 85th percentile. In fact, measuring it and comparing it to the posted speed limit provides the traffic planner with a valuable reality check."

So, a reality check would be based on numbers, not people?

» "The actual folly lies in always trying to accommodate motorized traffic, in believing that to be desirable or even possible."

The "always" is the disturbing part. The whole point of the article was that the pedestrian is left out of the equation. This means that we should beyond the accommodation of the motorized traffic to the safety (hence, accommodation perhaps) of the pedestrian.

» "Luckily we seem to be moving beyond that."

Can you please elaborate more on this.

» "Where do you find anything in there about speed limits? Let alone that increasing the speed limit would reduce the crash risk?"

You are correct and the word limit shouldn't be there. Thank you for pointing that out.

» " The graph does not endorse or justify speeding."

Where's that written on the text?

» "Solomon’s report deals with main rural highways. Look, it says so right on the front page! How should it have any significance for pedestrians or cyclists?"

Yes, it says that. But that curve is still used nowadays. There's no need to do a whole research on the internet for that. The point is: why is it still considered as valid? You should be saying that to traffic engineers that use that curve to justify some speed limits on non-rural highways, not me.

All in all, I liked your comment a lot. It only lacks references to corroborate some things, like the speed limits in Europe. Looking forward for your reply.

The crash risk curve is yet another of those correlation-without-questioning-causation graphs. 1964 or not, there's no reason to believe the correlation is wrong. It just fails to ask the right questions.

1 - What makes someone a slowest 30% driver? Some are just extra cautious. But many, probably most, are the kind of drivers more likely to get into a crash - the uncertain new drivers and the seniors that have slowed reaction times and dimming eyesight.

2 - What happens if you measure per 100,000 driving hours, instead of per 100,000,000 miles travelled? Slower drivers spend more time on the roads to accomplish the 100 million miles. If you get into any "is cycling dangerous" debates, you see the same kind of thing...per distance traveled, cycling is more dangerous than driving because it involves a lot more time exposed to the risks of modern roads to move the same distance. Of course, cyclists generally travel much smaller distances.

@Nadia Bee, thank you. Please keep visiting our website because we're writing something on that. In the mean time, do you have documentation on those subjects that you could kindly send it to me? My e-mail is in my profile link.

The academic transportation field sees a problem with the 85%ile approach. Check out the Norwegian Institute of Transport Economics paper in the journal Transport Policy, http://dx.doi.org/10.1016/j.tranpol.2009.12.006

@RL: "The folly does not lie in using the 85th percentile. In fact, measuring it and comparing it to the posted speed limit provides the traffic planner with a valuable reality check. "

Why the 85th Percentile?

@RL: "What this diagram [Solomon Curve] actually says is that cars are more at risk when traveling much faster or much slower than all the other cars on that road. That sounds about right, at least for the main rural highways that Solomon’s report covers."

Pedro Madruga misinterprets that graph (http://www.flickr.com/photos/16nine/8189404347/), which actually refers to deviation from average speed, but it is not "about right" to suggest that vehicles moving much slower than "all the other cars" on a road are at increased risk. The key variable to be considered is average (mean) speed.

Outdated and long-discredited research dating back to the 1960s and 1970s is still regurgitated, without proper analysis, by people who campaign against speed cameras and such. Pseudoscientific gobbledegook is their preferred language, often augmented with nonsensical graphs. The pseudoscientists just love the Solomon Curve. See here for a UK example of such pseudoscience: http://www.safespeed.org.uk

Later and better research, eg Kloeden et al 1997, also found a U-shaped speed-risk curve, but this conclusion has since been revised.

Among others, Rune Elvik has comprehensively demolished both the 85th Percentile and U-shaped curve myths. As Elvik and colleagues have pointed out, a U-shaped relationship between speed and rate of crash involvement could be a statistical artefact arising from errors in the measurement of speed. Even if the speed of vehicles involved in crashes is accurately measured in all cases, a U-shaped curve for deviation from mean speed can still arise purely as a statistical artefact. Elvik explains how in his seminal report, Speed and road accidents -- an evaluation of the Power Model. (https://www.toi.no/getfile.php/Publikasjoner/T%C3%98I%20rapporter/2004/740-2004/740-2004.pdf)

That said, the research on speed and risk continues to evolve: https://www.toi.no/getfile.php/Publikasjoner/T%C3%98I%20rapporter/2009/1034-2009/1034-2009-nett.pdf

Oh man, this is a great post. Thank you so much. Our Traffic engineers will not even hear about reducing speed limits on our narrow neighborhood streets below 30mph because it would be too dangerous according to the solomon curve—ridiculous.

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